1. Field of the Invention
The present invention relates to a signal processing method adapted to search an optimum solution in a neural network which is applicable to problems in processing a variety of intelligent information.
2. Description of the Prior Art
It is noted of late that various attempts are in rapid progress with regard to a contrivance of incorporating the biological information processing mechanism of life into an engineering information processing system. The studies of neural networks have been developed with such background, and some models thereof are currently spreading among the general engineering, inclusive of a learning algorithm of error back propagation, Hopfield neural network and so forth. Examining such neural network models from the dynamic point of view, it is understood that they are based on the premise of the Liapunov stability in common. More specifically, the process of learning or memory recall is defined as dynamics of asymptotic convergence from an adequate initial value on a given energy phase toward an equilibrium point attractor. The equilibrium point attained through such process is a relative minimum solution of the energy and may not exactly be a desired minimum or optimum solution to be obtained, thereby raising a problem of local minimum. It is ideal to achieve a stable descent along the energy gradient while averting the local minimum solution successfully, but such is not realizable in any model dominated by the Liapunov stability.
Describing the above in further detail, it has been customary heretofore to employ a steepest descent method when searching a minimum solution in the presence of some local minimum solution. According to such known steepest descent method, in a case where a minimizing evaluation function E is given by
E=(x.sub.1, x.sub.2 . . . . x.sub.n)
partial differential values to a variable x in the local points of the evaluation function E are calculated as follows: ##EQU1## where .epsilon. is a positive constant.
Temporally solving the above evolutional equations numerically with respect to the variable x, the minimum solution can be obtained by utilizing the Liapunov stability that the variable x is at the minimum solution when the partial differential value x has reached zero (i.e., when the change of the partial differential value x has become none).
However, a desired solution to be finally obtained is the minimum (optimum) solution as shown in FIG. 24, and the local minimum solution is not exactly coincident with the minimum solution, so that a restriction is existent in calculating the minimum solution (optimum solution) by the steepest descent method.
Therefore a new dynamic premise may be contrived to render the minimum absorption structure unstable by partially altering the premise of the Liapunov stability.
Reexamining the neural net dynamics from the viewpoint mentioned above, a chaotic dynamic system is considered to replace the dynamic system of the Liapunov stability. The path realized by the chaotic dynamic system has some unpredictable instability while being led to an attractor, so that both stability and instability are coexistent in the dynamics. In case such chaotic characteristic is introduced into a neural network, it is expectable to furnish the network model with enhanced flexibility. With regard to applications of the chaotic dynamics to neural networks, noticeable results have been attained heretofore due to the advanced studies based particularly on the biological researches.
In "Pattern Dynamics of Chaotic Neural Network" (Shingaku Giho, NC89-8, 43 (1989)), there is proposed a mathematic model of a chaotic neural network accomplished on the basis of the analytic result relative to the nonlinear response characteristic observed in the large axon of a squid. Also in "Memory Dynamics in Asynchronous Neural Networks" (Prog. Theor. Phys. 78 (1987) 51) and "Information Processing of Brain and Chaos" (Computer Today, 23 (1989) No. 32), a network model is constructed for realizing chaotic memory search with disclosure of a role in the chaotic information processing by an elucidatory approach of brain based on observation of the column structure of the cerebral cortex of a sea bream.
However, any of the above conventional methods has some difficulties in efficiently obtaining the minimum solution (optimum solution) out of a plurality of local minimum solutions.